渐近线性四阶半正边值问题正解的分歧结构

运用分歧理论和拓扑度理论研究四阶两点半正边值问题{x″″(t)=λf(t,x(t)),t∈(0,1),x(0)=x(1)=x″(0)=x″(1)=0正解的存在性,其中:λ>0为参数;f:[0,1]×[0,+∞)→R连续.获得了该问题在非线性项满足无穷远处渐近线性增长条件下正解存在性的新结果.

四阶半正超线性边值问题正解的存在性

在不要求非线性项f(x,y)连续且下方有界的情况下,证明了当f满足Carath啨odory条件时四阶半正边值问题正解的存在性.

An Existence Theorem of Positive Solution for Fourth-order Superlinear Semipositone Eigenvalue Problems

In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.